Phase-Locked loops lock-in range in Frequency Modulated-Atomic Force Microscope nonlinear control system |
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Authors: | Átila Madureira Bueno José Manoel Balthazar |
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Institution: | a Universidade Estadual Paulista “Júlio de Mesquita Filho”, Departamento de Estatística, Matemática Aplicada e Computação, DEMAC, Avenida 24A, 1515, Bela Vista, 13506-900, Rio Claro, SP, Brazil b Escola Politécnica da Universidade de São Paulo, Departamento de Telecomunicações e Controle, PTC, Brazil |
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Abstract: | Since the mid 1980s the Atomic Force Microscope is one the most powerful tools to perform surface investigation, and since 1995 Non-Contact AFM achieved true atomic resolution. The Frequency-Modulated Atomic Force Microscope (FM-AFM) operates in the dynamic mode, which means that the control system of the FM-AFM must force the microcantilever to oscillate with constant amplitude and frequency. However, tip-sample interaction forces cause modulations in the microcantilever motion. A Phase-Locked loop (PLL) is used to demodulate the tip-sample interaction forces from the microcantilever motion. The demodulated signal is used as the feedback signal to the control system, and to generate both topographic and dissipation images. As a consequence, a proper design of the PLL is vital to the FM-AFM performance. In this work, using bifurcation analysis, the lock-in range of the PLL is determined as a function of the frequency shift (Ω) of the microcantilever and of the other design parameters, providing a technique to properly design the PLL in the FM-AFM system. |
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Keywords: | Frequency-Modulated Atomic Force Microscopy Phase-Locked loops Bifurcation Nonlinear dynamics Mathematical model |
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